Irrational base discrete weighted transform

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the irrational base discrete weighted transform (IBDWT) is a variant of the <a href="/facts/Fast_Fourier_transform/caT7UUCh">fast Fourier transform</a> using an <a href="/facts/Irrational_number/Psv19TET">irrational</a> base; it was developed by <a href="/facts/Richard_Crandall/asxnT8bD">Richard Crandall</a> (<a href="/facts/Reed_College/ASQU5Dlf">Reed College</a>), Barry Fagin (<a href="/facts/Dartmouth_College/JLk2nNaN">Dartmouth College</a>) and Joshua Doenias (<a href="/facts/NeXT/qcCmhJl3">NeXT Software</a>) in the early 1990s using <a href="/facts/Mathematica/dRwoGFG2">Mathematica</a>.
The IBDWT is used in the <a href="/facts/Great_Internet_Mersenne_Prime_Search/vuF5SW9X">Great Internet Mersenne Prime Search</a>'s client <a href="/facts/Prime95/gyjjG3l3">Prime95</a> to perform <a href="/facts/FFT_multiplication/68xf6EdK">FFT multiplication</a>, as well as in other programs implementing <a href="/facts/Lucas%25E2%2580%2593Lehmer_primality_test/P6sD2wv8">Lucas–Lehmer test</a>, such as CUDALucas and Glucas.

<ul><li><a href="/facts/Richard_Crandall/asxnT8bD">Richard Crandall</a>, Barry Fagin: Discrete weighted transforms and large-integer arithmetic, Mathematics of Computation 62, 205, 305-324, January 1994 (<a href="http://www.faginfamily.net/barry/Papers/Discrete%20Weighted%20Transforms.pdf">PDF file</a>)</li>
<li><a href="/facts/Richard_Crandall/asxnT8bD">Richard Crandall</a>: Topics in Advanced Scientific Computation, TELOS/Springer-Verlag</li></ul>

Irrational base discrete weighted transform open-in-new

Irrational base discrete weighted transform